Solution landscapes of the simplified Ericksen--Leslie model and its comparison with the reduced Landau--de Gennes model

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Han, Yucen and Yin, Jianyuan and Hu, Yucheng and Majumdar, Apala and Zhang, Lei (2021) Solution landscapes of the simplified Ericksen--Leslie model and its comparison with the reduced Landau--de Gennes model. Proceedings of the Royal Society Part A - Mathematical, Physical and Engineering Sciences, 477 (2253). 20210458. ISSN 1471-2962 (https://doi.org/10.1098/rspa.2021.0458)

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Abstract

We investigate the solution landscapes of a simplified Ericksen--Leslie (sEL) vector model for nematic liquid crystals, confined in a two-dimensional square domain with tangent boundary conditions. An efficient numerical algorithm is developed to construct the solution landscapes by utilizing the symmetry properties of the model and the domain. Since the sEL model and the reduced Landau--de Gennes (rLdG) models can be viewed as Ginzburg--Landau functionals, we systematically compute the solution landscapes of the sEL model, for different domain sizes, and compare with the solution landscapes of the corresponding rLdG models. There are many similarities, including the stable diagonal and rotated states, bifurcation behaviors, and sub-solution landscapes with low-index saddle solutions. Significant disparities also exist between the two models. The sEL vector model exhibits the stable solution $C\pm$ with interior defects, high-index "fake defects" solutions, novel tessellating solutions, and certain types of distinctive dynamical pathways. The solution landscape approach provides a comprehensive and efficient way for model comparison and is applicable to a wide range of mathematical models in physics.

ORCID iDs

Han, Yucen, Yin, Jianyuan, Hu, Yucheng, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Zhang, Lei;
  • Item type:Article
    ID code:77899
    Dates:
    Date
    Event
    29 September 2021
    Published
    8 September 2021
    Published Online
    5 August 2021
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:23 Sep 2021 15:26
    Last modified:11 Nov 2024 13:14
    URI:https://strathprints.strath.ac.uk/id/eprint/77899
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